The invention relates to a pumping apparatus for delivering liquid at a high pressure, in particular a pumping apparatus for solvent delivery in liquid chromatography or supercritical fluid chromatography. The pumping apparatus pumps a mobile phase and a sample to be separated through the chromatographic system which includes a separation column and various transfer lines.
In chromatographic analysis, the flow rate of the liquid delivered to the column should be adjustable over a wide range. Once adjusted, it is very important to keep the flow rate constant as fluctuations cause variations in the retention time and associated areas under chromatographic peaks generated by chromatographic detectors of the separated sample. Flow sensitive detectors used in supercritical fluid or liquid chromatography include RI detectors, dielectric constant detectors, electrical conductivity detectors, NPD, ECD and fluorescence detectors. Since the area under the peaks are representative of the concentration of the chromatographically separated sample substances, fluctuations in the flow rate would impair the accuracy and the reproducibility of quantitative measurements. Additionally, many detectors are sensitive to flow and/or pressure ripples.
The compressibility of chromatographic solvents becomes noticeable at the high pressures encountered in high performance liquid chromatography and supercritical fluid chromatography. Such compressibility results in an additional source of fluctuations in the flow rate as the piston must compress the liquid to its final delivery pressure before actual delivery of liquid starts. This results in the outflow having pulsations which occur at the frequency of the pump. The percent magnitude of pulsations remains substantially constant over a wide range of flow rates, however, as the amplitudes of the peaks in the chromatogram become smaller at low flow rates, the influence of pulsations on the chromatographic results is more pronounced.
It is known to use a dual piston pump having two interconnected pump heads each with a reciprocating piston. The pistons may be driven via cams and a cam-shaft, a ball-screw drive or any other suitable mechanism which permits a phase difference resulting in a comparatively smooth outflow. A dual piston pump driven via cams and a common cam shaft is known from U.S. Pat. No. 4,352,636. One type of reciprocating pump which incorporates the ball-screw drive is disclosed in U.S. Pat. No. 4,883,409 entitled "Pumping Apparatus for Delivering Liquid at High Pressure", and is hereby incorporated by reference. As set forth in FIG. 1 the '409 patent discloses a pumping apparatus having two gear driven pistons which reciprocate in opposite directions in two pump chambers, respectively. The pistons are coupled to ball-screw drives which translate the rotary motion of the spindles into a linear motion of the pistons. The stroke volume can be changed by changing the amount in which the spindles are rotated during a pump cycle. Furthermore, a ball-screw drive permits the selection of any desired piston displacement over time during a pump cycle. For example, the displacement may be varied linearly as a function of time or accelerated for a short time to obtain a pre-compression phase.
FIG. 2(a) illustrates the beginning of the intake cycle for a known ball-screw, dual chamber reciprocating pump illustrated in FIG. 1 in which the output of the primary pump chamber is connected via a valve to the input of the secondary pump chamber. The stroke of each piston can be varied by controlling the angle of rotation of a reversible drive motor. The gear ratio is chosen to allow the primary piston to sweep twice as much volume as the secondary piston. If the primary and secondary cylinders have the same diameter, then the primary piston must move twice as fast as the secondary piston. Thus, if the primary piston has a volumetric stroke of L, the secondary piston will have a volumetric stroke of L/2. The outlet pressure can be kept constant at P.sub.o using a back pressure regulator or a flow restrictor.
The pumping cycle for this pump is set forth in FIG. 2(b). As the primary piston moves downward, the primary pressure decreases causing check valve 10 to open and check valve 20 to close, thus sucking in a fluid volume equal to L from the inlet. At the same time, the secondary piston delivers a volume of liquid (L/2) to the outlet. The pump motor then changes direction and the primary piston moves upward delivering a volume L. One half of this volume (L/2) is delivered to the outlet, and the other half is used to fill the vacuum generated in the secondary cylinder due to its downward motion. Assuming the fluid is incompressible, a flow of L/cycle is maintained in accordance to FIG. 3(a)-3(d). The volumetric flow rate F.sub.v for incompressible fluids can be expressed as follows: EQU F.sub.v =L.times.f.sub.i (Volume per unit Eqn ( 1) time)
Where:
F.sub.v =Volumetric flow rate at a defined outlet pressure PA1 f.sub.i =Pump frequency in cycles per unit time required to maintain flow rate of F.sub.v when pumping incompressible fluids. PA1 L=Primary piston stroke volume PA1 .rho..sub.o =Fluid density at the outlet pressure. Assumed constant for incompressible fluids at all pressures and temperatures.
The mass flow rate F.sub.m can be expressed as: EQU F.sub.m =.rho..sub.i .times.F.sub.v =.rho..sub.i .times.L.times.f.sub.i (Mass per unit Eqn ( 2) time)
Where:
Since real fluids are compressible, Eqn 1 and Eqn 2 do not correctly set forth the volumetric flow rate and mass flow rate of a reciprocating pump. Furthermore, the compressibility of the fluid is a function of both pressure and temperature. Liquid chromatography and supercritical fluid chromatography systems typically treat these compressibility factors as constants, however, they vary considerably.